The maximum index of signed complete graphs whose negative edges induce a bicyclic graph
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916380233695232 |
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| author | Fang, Ziyi Chen, Fan Yuan, Xiying |
| author_facet | Fang, Ziyi Chen, Fan Yuan, Xiying |
| contents | Let $Γ=(K_n,H)$ be a signed complete graph whose negative edges induce a subgraph $H$. Let $A(Γ)$ be the adjacency matrix of the signed graph $Γ$. The largest eigenvalue of $A(Γ)$ is called the index of $Γ$. In this paper, the index of all the signed complete graphs whose negative edges induce a bicyclic graph $B$ is investigated. Specifically, the structure of the bicyclic graph $B$ such that $Γ=(K_n,B)$ has the maximum index is determined. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_01923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximum index of signed complete graphs whose negative edges induce a bicyclic graph Fang, Ziyi Chen, Fan Yuan, Xiying Combinatorics Let $Γ=(K_n,H)$ be a signed complete graph whose negative edges induce a subgraph $H$. Let $A(Γ)$ be the adjacency matrix of the signed graph $Γ$. The largest eigenvalue of $A(Γ)$ is called the index of $Γ$. In this paper, the index of all the signed complete graphs whose negative edges induce a bicyclic graph $B$ is investigated. Specifically, the structure of the bicyclic graph $B$ such that $Γ=(K_n,B)$ has the maximum index is determined. |
| title | The maximum index of signed complete graphs whose negative edges induce a bicyclic graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.01923 |